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(3x+5)(5x+3)=x
We move all terms to the left:
(3x+5)(5x+3)-(x)=0
We add all the numbers together, and all the variables
-1x+(3x+5)(5x+3)=0
We multiply parentheses ..
(+15x^2+9x+25x+15)-1x=0
We get rid of parentheses
15x^2+9x+25x-1x+15=0
We add all the numbers together, and all the variables
15x^2+33x+15=0
a = 15; b = 33; c = +15;
Δ = b2-4ac
Δ = 332-4·15·15
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{21}}{2*15}=\frac{-33-3\sqrt{21}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{21}}{2*15}=\frac{-33+3\sqrt{21}}{30} $
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